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The third of Maxwell's equations is called the [[Ampere-maxwell law|Ampère–Maxwell law]]. It states that a magnetic field can be generated by an [[electric current]].<ref>{{Cite web|title=Ampere's Law|url=http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/amplaw.html|access-date=2020-11-27|website=hyperphysics.phy-astr.gsu.edu}}</ref> The direction of the magnetic field is given by Ampère's [[right-hand grip rule]]. If the wire is straight, then the magnetic field is curled around it like the gripped fingers in the right-hand rule. If the wire is wrapped into coils, then the magnetic field inside the coils points in a straight line like the outstretched thumb in the right-hand grip rule.<ref>{{Cite book|last=Grant, I. S. (Ian S.)|url=https://www.worldcat.org/oclc/21447877|title=Electromagnetism|date=1990|publisher=Wiley|others=Phillips, W. R. (William Robert)|isbn=0-471-92711-2|edition=2nd|series=The Manchester Physics Series|___location=Chichester [England]|pages=125|oclc=21447877}}</ref> When electric currents are used to produce a [[magnet]] in this way, it is called an [[electromagnet]]. Electromagnets often use a wire curled up into [[solenoid]] around an iron core which strengthens the magnetic field produced because the iron core becomes magnetised.<ref name=":8">{{Cite web|title=Magnets and Electromagnets|url=http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/elemag.html#c1|access-date=2020-11-27|website=hyperphysics.phy-astr.gsu.edu}}</ref><ref name=":9">{{Cite web|title=Ferromagnetism|url=http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/ferro.html#c4|access-date=2020-11-27|website=hyperphysics.phy-astr.gsu.edu}}</ref> Maxwell's extension to the law states that a time-varying electric field can also generate a magnetic field.<ref name=":5" /> Similarly, [[Faraday's law of induction]] states that a magnetic field can produce an electric current. For example, a magnet pushed in and out of a coil of wires can produce an electric current in the coils which is proportional to the strength of the magnet as well as the number of coils and the speed at which the magnet is inserted and extracted from the coils. This principle is essential for [[transformer]]s which are used to transform currents from high [[voltage]] to low voltage, and vice versa. They are needed to convert high voltage [[mains electricity]] into low voltage electricity which can be safely used in homes. Maxwell's formulation of the law is given in the [[Maxwell–Faraday equation]]—the fourth and final of Maxwell's equations—which states that a time-varying magnetic field produces an electric field.
[[File:EM_Spectrum_Properties_edit.svg|thumb|440x440px|The [[electromagnetic spectrum]]
Together, Maxwell's equations provide a single uniform theory of the electric and magnetic fields and Maxwell's work in creating this theory has been called "the second great unification in physics" after the first great unification of [[Newton's law of universal gravitation]].<ref>{{Cite journal|last=Editors|first=AccessScience|date=2014|title=Unification theories and a theory of everything|url=https://www.accessscience.com/content/unification-theories-and-a-theory-of-everything/BR0814141|journal=Access Science|language=en|doi=10.1036/1097-8542.BR0814141}}</ref> The solution to Maxwell's equations in [[free space]] (where there are no charges or currents) produces [[wave equation]]s corresponding to [[electromagnetic waves]] (with both electric and magnetic components) travelling at the [[speed of light]].<ref>{{Cite book|last=Grant, I. S. (Ian S.)|url=https://www.worldcat.org/oclc/21447877|title=Electromagnetism|date=1990|publisher=Wiley|others=Phillips, W. R. (William Robert)|isbn=0-471-92711-2|edition=2nd|series=The Manchester Physics Series|___location=Chichester [England]|pages=365|oclc=21447877}}</ref> The observation that these wave solutions had a wave speed exactly equal to the speed of light led Maxwell to hypothesise that light is a form of electromagnetic radiation and to posit that other electromagnetic radiation could exist with different wavelengths.<ref name="ADTEF">{{cite journal|last=Maxwell|first=James Clerk|year=1865|title=A dynamical theory of the electromagnetic field|url=http://upload.wikimedia.org/wikipedia/commons/1/19/A_Dynamical_Theory_of_the_Electromagnetic_Field.pdf|url-status=live|journal=Philosophical Transactions of the Royal Society of London|volume=155|pages=459–512|bibcode=1865RSPT..155..459C|doi=10.1098/rstl.1865.0008|archive-url=https://web.archive.org/web/20110728140123/http://upload.wikimedia.org/wikipedia/commons/1/19/A_Dynamical_Theory_of_the_Electromagnetic_Field.pdf|archive-date=28 July 2011|quote=Light and magnetism are affections of the same substance (p.499)|s2cid=186207827}}</ref> The existence of electromagnetic radiation was proved by [[Heinrich Hertz]] in a series of experiments ranging from 1886 to 1889 in which he discovered the existence of [[radio wave]]s. The full [[electromagnetic spectrum]] (in order of increasing frequency) consists of radio waves, [[microwave]]s, [[Infrared|infrared radiation]], [[visible light]], [[Ultraviolet|ultraviolet light]], [[X-ray]]s and [[gamma ray]]s.<ref>{{Cite web|date=2011-08-25|title=Introduction to the Electromagnetic Spectrum and Spectroscopy {{!}} Analytical Chemistry {{!}} PharmaXChange.info|url=https://pharmaxchange.info/2011/08/introduction-to-the-electromagnetic-spectrum-and-spectroscopy/|access-date=2020-11-26|website=pharmaxchange.info|language=en-US}}</ref>
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=== Capacitors ===
[[File:Parallel plate capacitor.svg|thumb|A parallel plate capacitor
A [[capacitor]] is an [[electronic component]] that stores electrical potential energy in an electric field between two oppositely charged conducting plates. If one of the conducting plates has a [[charge density]] of +''Q/A'' and the other has a charge of -''Q/A'' where ''A'' is the area of the plates, then there will be an electric field between them. The potential difference between two parallel plates ''V'' can be derived mathematically as<ref name=":11">{{Cite book|last=Grant, I. S. (Ian S.)|url=https://www.worldcat.org/oclc/21447877|title=Electromagnetism|date=1990|publisher=Wiley|others=Phillips, W. R. (William Robert)|isbn=0-471-92711-2|edition=2nd|series=The Manchester Physics Series|___location=Chichester [England]|pages=41–42|oclc=21447877}}</ref>
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[[Kirchhoff's circuit laws|Kirchhoff's junction rule]] states that the current going into a junction (or node) must equal the current that leaves the node. This comes from [[charge conservation]], as current is defined as the flow of charge over time. If a current splits as it exits a junction, the sum of the resultant split currents is equal to the incoming circuit.<ref name=":12">{{Cite book|last=Young, H. D., Freedman, R. A.|url=https://www.worldcat.org/oclc/897436903|title=Sears and Zemansky's University Physics with Modern Physics|publisher=[[Pearson PLC|Pearson]]|year=2016|isbn=978-0-321-97361-0|edition=14th|___location=Boston|pages=872–878|oclc=897436903}}</ref>
[[Kirchhoff's circuit laws|Kirchhoff's loop rule]] states that the sum of the voltage in a closed loop around a circuit equals zero. This comes from the fact that the electric field is [[Conservative vector field|conservative]] which means that no matter the path taken, the potential at a point
Rules can also tell us how to add up quantities such as the current and voltage in [[series and parallel circuits]].<ref name=":12" />
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